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If xy = 7 and x + y = 5, then find x^3 + y^3.

Jul 1, 2020

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If xy = 7 and x + y = 5, then find $$x^3 + y^3$$.

1.

$$\begin{array}{|rcll|} \hline (x + y)^2 &=& x^2+2xy+y^2 \\ 5^2 &=& x^2+2*7+y^2 \\ x^2+y^2 &=& 25-14 \\ \mathbf{x^2+y^2} &=& \mathbf{11} \\ \hline \end{array}$$

2.

$$\begin{array}{|rcll|} \hline (x^2+y^2)(x+y) &=& x^3+x^2y+y^2x+y^3 \\ 11*5 &=& x^3+y^3+xy(x+y) \\ 55 &=& x^3+y^3+7*5 \\ x^3+y^3 &=& 55 -35 \\ \mathbf{x^3+y^3} &=& \mathbf{20} \\ \hline \end{array}$$

Jul 2, 2020